Iwahori-spherical representations of GSp(4) and Siegel modular forms of degree 2 with square-free level

Abstract

A theory of local old- and newforms for representations of $GSp\left(4\right)$ over a $p$-adic field with Iwahori-invariant vectors is developed. The results are applied to Siegel modular forms of degree 2 with square-free level with respect to various congruence subgroups.